Ben-Sasson et al. [1]} used subspace polynomials to generate cyclic subspace codes with size \(\frac{q^n-1}{q-1}\)  and minimum distance \(2k-2\) . Precisely, they proved that Conjecture REF  holds true for any given \(k\)  and infinitely many values of \(n\) . Such result was then improved in [2]}.
However, the relation between \(k\)  and \(n\)  was not immediately clear, as \(n\)  depends on the degree of the irreducible factors of \(x^{q^k}+x^q+x\)  in \({\mathbb {F}}_q\) . Finally, Conjecture REF  was solved in [3]} for most of the cases, by using Sidon spaces.
